algebraic integer

代数整数

Number Theory · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A complex number satisfying a monic polynomial with coefficients in Z\mathbb Z.

满足某个首一整系数多项式的复数。

Example

(1+5)/2(1+\sqrt5)/2 satisfies X2−X−1=0X^2-X-1=0.

Usage and distinctions

An algebraic number need not be integral: 1/21/2 satisfies 2X−1=02X-1=0 but no monic integer polynomial.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. 张神星 — 代数数论讲义 v2.5 (2024-01-09)，合肥工业大学作者讲义Definitions 1.10 and 1.14, printed pages 6–7; monicity comes from Definition 1.10 · Checked 2026-10-14

Translation sources

  1. 张神星 — 代数数论讲义 v2.5 (2024-01-09)，合肥工业大学作者讲义定义1.14，printed page 7 代数整数；定义1.10，printed page 6 首一条件 · Checked 2026-10-14
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